The density of sets containing large similar copies of finite sets

DOI10.1007/s11854-022-0231-6OpenAlexW3088414833MaRDI QIDQ2680338

Alexia Yavicoli, Vjekoslav Kovač, Kenneth J. Falconer

Publication date: 29 December 2022

Published in: Journal d'Analyse Mathématique (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2007.03493

Mathematics Subject Classification ID

Length, area, volume, other geometric measure theory (28A75) Density, gaps, topology (11B05) Ramsey theory (05D10)

Related Items (1)

Incidence problems in harmonic analysis, geometric measure theory, and ergodic theory. Abstracts from the workshop held June 4--9, 2023

Cites Work

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• Finite configurations in sparse sets
• A note on configurations in sets of positive density which occur at all large scales
• On polynomial configurations in fractal sets
• Sequences, discrepancies and applications
• Distances in positive density sets in \(\mathbb R^d\)
• Arithmetic progressions in sets of fractional dimension
• A Szemerédi type theorem for sets of positive density in \(\mathbb R^k\)
• Recent trends in Euclidean Ramsey theory
• Distance sets corresponding to convex bodies
• Patterns in thick compact sets
• A Szemerédi-type theorem for subsets of the unit cube
• Distance graphs and sets of positive upper density in \(\mathbb{R}^d\)
• Existence of similar point configurations in thin subsets of \(\mathbb{R}^d\)
• Equilateral triangles in subsets of \(\mathbb{R}^d\) of large Hausdorff dimension
• Nilfactors of \(\mathbb R^m\) and configurations in sets of positive upper density in \(\mathbb R^m\)
• Simplices and sets of positive upper density in $\mathbb {R}^d$
• Plane Sets with Positive Density at Infinity Contain all Large Distances
• Product of Simplices and sets of positive upper density in ℝ^d
• Density theorems for anisotropic point configurations
• Weak hypergraph regularity and applications to geometric Ramsey theory
• Boxes, extended boxes and sets of positive upper density in the Euclidean space
• Sets in ℝ^{𝕕} with slow-decaying density that avoid an unbounded collection of distances
• On Side Lengths of Corners in Positive Density Subsets of the Euclidean Space
• A Roth‐type theorem for dense subsets of Rd

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